Skew Hadamard matrices of order 4 × 37 and 4 × 43
نویسندگان
چکیده
منابع مشابه
An Infinite Family of Skew Hadamard Matrices
It has been conjectured that iϊ-matrices and even skew iJ-matrices always exist for n divisible by 4. Constructions of both types of matrices have been given for particular values of n and also for various infinite classes of values (see [1] for the pertinent references). In [1] D. Blatt and G. Szekeres constructed for the first time a skew ίf-matrix of order 52. Their construction is summarize...
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In this paper we formalize three constructions for skew-Hadamard matrices from a Computational Algebra point of view. These constructions are the classical 4 Williamson array construction, an 8 Williamson array construction and a construction based on OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2), a 9-variable full orthogonal design of order 16. Using our Computational Algebra formalism in conjunction with...
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متن کاملFive new orders for Hadamard matrices of skew type
By using the (generalized) Goethals-Seidel array, we construct Hadamard matrices of skew type of order 4n for n = 81,103,151,169, and 463. Hadamard matrices of skew type for these orders are constructed here for the first time. Consequently the list of odd integers n < 300 for which no Hadamard matrix of skew type of order 4n is presently known is reduced to 45 numbers (see the comments after t...
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We construct Hadamard matrices of orders 4 · 251 = 1004 and 4 · 631 = 2524, and skewHadamard matrices of orders 4 · 213 = 852 and 4 · 631 = 2524. As far as we know, such matrices have not been constructed previously. The constructions use the GoethalsSeidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1992
ISSN: 0097-3165
DOI: 10.1016/0097-3165(92)90029-t